Regular Poisson manifolds of compact types (PMCT 2)
Regular Poisson manifolds of compact types (PMCT 2)
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紧凑型正则泊松流形 (PMCT 2)
DOI：
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发表时间：
2016
期刊：
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通讯作者：
D. Martínez
中科院分区：
文献类型：
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作者：
M. Crainic;R. Fernandes;D. Martínez
这是第二个文件的一系列致力于研究泊松结构的紧凑型（PMCT）。在本文中，我们专注于定期PMCT，表现出丰富的横向几何。我们证明了它们的叶空间是积分仿射轨道。我们证明了叶辛形式的上同调类线性变化，并有一个杰出的多项式函数描述的叶辛体积。PMCT的叶空间具有自然的Duistermaat-Heckman测度和Weyl型积分公式。我们引入了辛几何的概念，并且我们证明了它们阻碍了将PMCT实现为辛完全各向同性纤维化（a.k.a.~非交换可积系统）。
This is the second paper of a series dedicated to the study of Poisson structures of compact types (PMCTs). In this paper, we focus on regular PMCTs, exhibiting a rich transverse geometry. We show that their leaf spaces are integral affine orbifolds. We prove that the cohomology class of the leafwise symplectic form varies linearly and that there is a distinguished polynomial function describing the leafwise sympletic volume. The leaf space of a PMCT carries a natural Duistermaat-Heckman measure and a Weyl type integration formula holds. We introduce the notion of a symplectic gerbe, and we show that they obstruct realizing PMCTs as the base of a symplectic complete isotropic fibration (a.k.a.~a non-commutative integrable system).